Silviase/jgov_v1.4_full_ann huggingface dataset:
## 72 ) 民間最終消費支出デフレータ (消費税除く)

DEL(LOG(JA_PCP@),1) = C2001 * LOG(JA_PCP@.-1/(EXP(P2001+P2002*JA_TIMEV) * (SUM(JA_MK,0,19)/20)**P2003*JA_PMGS@**P2004))
+ C2002 * DEL(LOG(JA_PCP@.-1),1)
+ C2003 * DEL(LOG(JA_PCP@.-2),1)
+ C2004 * DEL(LOG(JA_PCP@.-3),1)
+ C2005 * DEL(LOG(JA_PCP@.-4),1)
+ C2006 * DEL(JA_GDPGAP.-2,1)
+ C2007 * DEL(JA_GDPGAP.-3,1)
+ C2008 * DEL(LOG(JA_FXS.-1),1)
+ C2009 * DEL(LOG(JA_FXS.-2),1)
+ C2010 * DEL(LOG(JA_WIPH),1)
+ C2011 * DEL(LOG(JA_WIPH.-1),1)
+ C2012 * DEL(LOG(JA_WIPH.-3),1)
+ C2013 * DEL(LOG(JA_IG/JA_GDP),1)
+ C2014 * DEL(LOG(JA_PFUEL@.-2),1)
+ C2015 * JA_D901
+ CERR * ER2_PCP@

## 73 ) 賃金俸給

JA\_WI = JA\_YWIV / JA\_LW

## 74 ) GDP デフレータ対前期差

JA_PGDPD = GR(JA_PGDP,1)*400

## 75 ) Unit Labor Cost

## 76 ) 個人企業所得

DEL(LOG(JA_YICV),1) = C2101 * LOG(JA_YICV.-1/(JA_YWV.-1**P2101 * EXP(P2102*JA_RCD.-1)))
+ C2102 * DEL(JA_CU.-1,1)
+ C2103 * DEL(JA_CU.-3,1)
+ C2104 * DEL(JA_UR.-1,1)
+ C2105 * DEL(LOG(JA_YWV.-1),1)
+ C2106 * DEL(LOG(JA_YWV.-2),1)
+ C2107 * JA_D001
+ CERR * ER2_YICV

## 77 ) 家計財産所得

JA_YIEV/(JA_NWCV.-1) = C2201 * 1

+ C2202 * 1/JA_NWCV.-1

+ C2203 * JA_NIV / (JA_NWCV.-1)

+ C2204 * GR(JA_PSHARE,4)*100

+ C2205 * JA_RCD

+ C2206 * JA_RCD.-1

+ C2207 * JA_RCD.-2

+ C2208 * JA_RGB.-1

+ C2209 * JA_RGB.-2

+ C2210 * JA_RGB.-3

+ C2211 * JA_RGB.-4

+ CERR * ER2_YIEV

## 78 ) 法人企業所得

JA_YCV+(JA_YIV+JA_CCAV-JA_TYCV) = (JA_NIV+JA_CCAV-JA_TYCV)-(JA_YWV+JA_YICV)

## 79 ) 法人企業所得 (税引後)

JA_YCVAT = SUM(JA_YCV,0,3)/4*(1-JA_ETT)
## 96 ) 純資産

JA_NWV = JA_FNWV + JA_KPV

## 97 ) 株式総額

JA SHARETV = JA PSHARE*JA RSHARET

## 98 ) 純資産 (家計保有分)

JA_NWCV = JA_FNWV + JA_LANDV + JA_SHAREV + JA_KHPV

## 99 ) 株式総額 (家計保有分)

JA_SHAREV = JA_PSHARE*JA_RSHARE

## 100 ）土地総額 (家計保有分)

JA_LANDV = JA_PLAND*JA_RLAND

## 101 ）個人税及び罰金、手数料

$$ \begin{array}{r l r l}

\mathrm{DEL}(\mathrm{LOG}(\mathrm{JA\_TYPV}+\mathrm{JA\_TPSV}),1)} & {=}& {C2701 * \mathrm{LOG}((\mathrm{EXP}(\mathrm{P2701})*(\mathrm{JA\_YWIV}.-1+\mathrm{JA\_YICV}.-1)**\mathrm{P2702}} \\

& & {* \mathrm{JA\_YIEV}.-1**\mathrm{P2703})/(\mathrm{JA\_TYPV}.-1+\mathrm{JA\_TPSV}.-1))} \\

& & {+ C2702 * \mathrm{DEL}(\mathrm{LOG}(\mathrm{JA\_YWIV}+\mathrm{JA\_YICV}),1)} \\

& & {+ C2703 * \mathrm{DEL}(\mathrm{LOG}(\mathrm{JA\_YWIV}.-2+\mathrm{JA\_YICV}.-2),1)} \\

& & {+ C2704 * \mathrm{DEL}(\mathrm{LOG}(\mathrm{JA\_YWIV}.-4+\mathrm{JA\_YICV}.-4),1)} \\

& & {+ C2705 * \mathrm{DEL}(\mathrm{LOG}(\mathrm{JA\_YIEV}.-1),1)} \\

& & {+ C2706 * \mathrm{DEL}(\mathrm{LOG}(\mathrm{JA\_YIEV}.-2),1)} \\

& & {+ C2707 * \mathrm{DEL}(\mathrm{LOG}(\mathrm{JA\_TYPV}.-1+\mathrm{JA\_TPSV}.-1),1)} \\

& & {+ CERR * \mathrm{ER2\_TYPV}}

\end{array} $$

## 102 ) 民間法人企業税及び罰金

JA_TYCV = JA_ETT * SUM(JA_YCV,0,3)/4

## 103 ) モデル上の法人実効税率

JA_ETT = (1.721055*JA_TT)/(1+6.522108*EXP(-2.975028*JA_ETT.-1+7.413776*(JA_YCV/JA_GDPV)-0.013053*JA_CU)) + JA_ETTERR

## 104 ) 消費税

$$ \begin{aligned}LOG(JA\_TCIV)\quad=&C2801*LOG(JA\_RTCI/(1+JA\_RTCI*JA\_PRTCPCP)*JA\_CPV\\&+JA\_RTCI/(1+JA\_RTCI*JA\_PRTCPIH)*JA\_IHPV+JA\_RTCI/(1+JA\_RTCI*JA\_PRTCPCG)*JA\_CGV\\&+JA\_RTCI/(1+JA\_RTCI*JA\_PRTCPIG)*JA\_IGV)\\&+C2802*JA\_DTCIC1*LOG(JA\_RTCI/(1+JA\_RTCI*JA\_PRTCPCP)*JA\_CPV\\&+JA\_RTCI/(1+JA\_RTCI*JA\_PRTCPIH)*JA\_IHPV+JA\_RTCI/(1+JA\_RTCI*JA\_PRTCPCG)*JA\_CGV\\&+JA\_RTCI/(1+JA\_RTCI*JA\_PRTCPIG)*JA\_IGV)\\&+C2803*JA\_DTCIC2*LOG(JA\_RTCI/(1+JA\_RTCI*JA\_PRTCPCP)*JA\_CPV\\&+JA\_RTCI/(1+JA\_RTCI*JA\_PRTCPIH)*JA\_IHPV+JA\_RTCI/(1+JA\_RTCI*JA\_PRTCPCG)*JA\_CGV\\&+JA\_RTCI/(1+JA\_RTCI*JA\_PRTCPIG)*JA\_IGV)\\&+C2804*JA\_D972C\\&+CERR*ER2\_TCIV\end{aligned} $$

## 105 ) その他関税

$$ \begin{aligned}DEL(LOG(JA_{-}OITAXV),1)&=C2901*1\\&+C2902*LOG((JA_{-}GDPV.-1+JA_{-}MFUELV.-1)/JA_{-}OITAXV.-1)\\&+C2903*DEL(LOG(JA_{-}MFUELV),1)\\&+C2904*DEL(LOG(JA_{-}MFUELV.-1),1)\\&+CERR*ER2_{-}OITAXV\\ \end{aligned} $$

## 106 ) 間接税

JA_ITAXV = JA_TCIV + JA_TCSTV + JA_OITAXV
## 107 ）一般政府財產所得

JA_YIGV/JA_SBGV.-1 = C3001 * 1
+ C3002 * JA_RGB
+ C3003 * JA_RGB.-1
+ C3004 * JA_RGB.-2
+ C3005 * JA_RGB.-3
+ C3006 * JA_YIGV.-1/JA_SBGV.-2
+ C3007 * JA_D941
+ C3008 * JA_D943
+ C3009 * JA_D951
+ C3010 * JA_D953
+ C3011 * JA_D894
+ CERR * ER2_YIGV

## 108 ）社会保障給付

$$ \begin{array}{r l}{\mathrm{L O G(J A\_{B} S S V)}}&{=\mathrm{C3101*1}}\\ &{+\mathrm{C3102*L O G(J A\_{S} B*J A\_{W} I P H*J A\_{P} O P65)}}\\ &{+\mathrm{C3103*L O G(J A\_{W} I P H*J A\_{U} R*J A\_{L} F/100)}}\\ &{+\mathrm{C3104*J A\_{D}901}}\\ &{+\mathrm{C E R R*E R2\_{B} S S V}}\end{array} $$

## 109 ）社会保障负担

$$ DEL(LOG(JA\_CSSV),1) = C3201 * LOG(JA\_CSSV.-1/(EXP(P3201)*(JA\_SR.-1*JA\_YWIV.-1)**P3202)) + C3202 * DEL(LOG(JA\_SR*JA\_YWIV),1) + C3203 * DEL(LOG(JA\_CSSV .-2),1) + CERR * ER2\_CSSV $$

## 110 ）期待租税负担率

$$ \log(JA\_PTAX) = T0101 + (T0120 + T0121 + T0122 + T0123) \times 100 $$

$$ + T0102 \times JA\_TIMEV $$

$$ + T0103 \times \log(JA\_JA\_SBGV.-5/(JA\_GDPPOT.-4 \times JA\_PGDP.-4)) $$

$$ + T0104 \times \log(JA\_JA\_SBGV.-6/(JA\_GDPPOT.-5 \times JA\_PGDP.-5)) $$

$$ + T0105 \times \log(JA\_JA\_SBGV.-7/(JA\_GDPPOT.-6 \times JA\_PGDP.-6)) $$

$$ + T0106 \times \log(JA\_JA\_SBGV.-8/(JA\_GDPPOT.-7 \times JA\_PGDP.-7)) $$

$$ + T0107 \times \log(JA\_JA\_SBGV.-9/(JA\_GDPPOT.-8 \times JA\_PGDP.-8)) $$

$$ + T0108 \times \log(JA\_JA\_SBGV.-10/(JA\_GDPPOT.-9 \times JA\_PGDP.-9)) $$

$$ + T0109 \times \log(JA\_JA\_SBGV.-11/(JA\_GDPPOT.-10 \times JA\_PGDP.-10)) $$

$$ + T0110 \times \log(JA\_JA\_SBGV.-12/(JA\_GDPPOT.-11 \times JA\_PGDP.-11)) $$

$$ + T0111 \times \log(JA\_JA\_SBGV.-13/(JA\_GDPPOT.-12 \times JA\_PGDP.-12)) $$

$$ + T0112 \times \log(JA\_JA\_SBGV.-14/(JA\_GDPPOT.-13 \times JA\_PGDP.-13)) $$

$$ + T0113 \times \log(JA\_JA\_SBGV.-15/(JA\_GDPPOT.-14 \times JA\_PGDP.-14)) $$

$$ + T0114 \times \log(JA\_JA\_SBGV.-16/(JA\_GDPPOT.-15 \times JA\_PGDP.-15)) $$

$$ + T0115 \times \log(JA\_JA\_SBGV.-17/(JA\_GDPPOT.-16 \times JA\_PGDP.-16)) $$

$$ + T0116 \times \log(JA\_JA\_SBGV.-18/(JA\_GDPPOT.-17 \times JA\_PGDP.-17)) $$

$$ + T0117 \times \log(JA\_JA\_SBGV.-19/(JA\_GDPPOT.-18 \times JA\_PGDP.-18)) $$

$$ + T0118 \times \log(JA\_JA\_SBGV.-20/(JA\_GDPPOT.-19 \times JA\_PGDP.-19)) $$

$$ + T0119 \times \log(JA\_JA\_SBGV.-21/(JA\_GDPPOT.-20 \times JA\_PGDP.-20)) $$

## 111 ）租税総額

$$ \begin{array}{r l}{\mathrm{J A\_{T} A X V}}&{{}=\mathrm{J A\_{T} Y P V}+\mathrm{J A\_{T} Y C V}+\mathrm{J A\_{I} T A X V}}\end{array} $$

## 112 ) 関税

JA TCSTV = JA RTCST * JA MGSV

113) 一般政府財政バランス

JA_BGV = JA_TAXV + JA_CSSV + JA_YIGV + JA_OTNGV - JA_CGV - JA_IGV - JA_BSSV - JA_SUBV

## 114 ）一般政府累積財政赤字

JA_SBGV = JA_SBGV.1 - JA_BGV/4 + JA_RSBGV
115) 一般政府財政バランス対名目 GDP 比 JA_BGV@GDPV = JA_BGV/JA_GDPV*100

116）一般政府累積財政赤字對名目 GDP 比 JA_SBGV@GDPV = JA_SBGV/JA_GDPV*400

117) マネ-サプライ (M2+CD, 平均残高)

$$ \text{DEL}(\text{LOG}(\text{JA\_M2CD}),1) = \text{C3301} \times 1 $$

$$ + \text{C3302} \times \text{LOG}(\text{JA\_M2CD}.-1/(\text{EXP}(\text{P3301}) \times \text{JA\_GDPV}.-1^{**}\text{P3302})) $$

$$ + \text{C3303} \times \text{LOG}(\text{JA\_NWCV}.-1/\text{JA\_M2CD}.-1) $$

$$ + \text{C3304} \times \text{DEL}(\text{LOG}(\text{JA\_GDPV}),1) $$

$$ + \text{C3305} \times \text{DEL}(\text{LOG}(\text{JA\_GDPV}.-1),1) $$

$$ + \text{C3306} \times \text{DEL}(\text{LOG}(\text{JA\_GDPV}.-2),1) $$

$$ + \text{C3307} \times \text{JA\_RCD} $$

$$ + \text{C3308} \times \text{JA\_D901C902} $$

$$ + \text{C3309} \times \text{JA\_D974C981} $$

$$ + \text{C3310} \times \text{JA\_D983C} $$

$$ + \text{CERR} \times \text{ER2\_M2CD} $$

118) マーシャルのK

JA_MK = JA_M2CD/JA_GDP

119) CD レード名目)

JA_RCD = MAX(C3351*1+C3352*GRY(JA_DPI@)*100+C3353*GRY(JA_PSHARE)*100 + C3354*(JA_GDPGAP-100)+C3355*JA_RCD.-1+JA_ERRRCD,0.03)

## 120 ) CD レート(実質)

JA_RRCD = JA_RCD - GR(JA_PGDP@,4)*100

## 121 ）公定歩合

DEL(JA_RDIS,1) = C3401 * DEL(JA_RCD,1)

+ C3402 * DEL(JA_RCD.-1,1)

+ C3403 * DEL(JA_RCD.-2,1)

+ C3404 * DEL(JA_RCD.-3,1)

+ CERR * ER2_RDIS

## 122 ）利付国債利回り(10年物）

JA_RGB = C3501 * 1
+ C3502 * SUM(JA_RCD, 1, 19) / 19
+ C3503 * JA_RCD
+ C3504 * GR(JA_PCP@, 1) * 400
+ C3505 * GR(JA_PCP@. - 1, 1) * 400
+ C3506 * GR(JA_PCP@. - 2, 1) * 400
+ CERR * ER2_RGB

## 123 ）東証株価指数

$$ \text{DEL}(\text{LOG}(\text{JA\_PSHARE}),1) = \text{C3601} * \log(\text{JA\_PSHARE}.-1/(\text{EXP}(\text{P3601}+\text{P3602}*\text{JA\_RCD}.-1)*\text{JA\_PGDP}**\text{P3603}*SUM(\text{JA\_YCVAT},0,11)**\text{P3604})) $$

$$ + \text{C3602} * \text{DEL}(\text{LOG}(\text{JA\_PSHARE}.-1),1) $$

$$ + \text{C3603} * \text{DEL}(\text{LOG}(\text{JA\_PSHARE}.-3),1) $$

$$ + \text{C3604} * \text{DEL}(\text{LOG}(\text{JA\_YCV}),1) $$

$$ + \text{C3605} * \text{DEL}(\text{LOG}(\text{JA\_M2CD}),1) $$

$$ + \text{C3606} * \text{DEL}(\text{LOG}(\text{JA\_M2CD}.-2),1) $$

$$ + \text{C3607} * \text{DEL}(\text{JA\_RGB},1) $$

$$ + \text{CERR} * \text{ER2\_PSHARE} $$
$$ \begin{aligned}JA\_{U}CCDE2&=JA\_{P}IFP@*({(1-JA\_{P}ER*JA\_{R}OR/100*JA\_{C}RH)/JA\_{P}ER/(1-JA\_{C}RH)}*100\\&\quad-P3951*SUM(GRY(JA\_{P}IFP@)*100,0,1)/2)*(1-JA\_{T}T*JA\_{P}VDP-JA\_{T}INCR)/(1-JA\_{T}T)\end{aligned} $$

## 124 ）株価收益率

DEL(LOG(1/JA_PER),1) = C3701 * 1
+ C3702 * LOG((1/JA_PER.-1)/(JA_YCV.-1/JA_SHARETV.-1))
+ C3703 * DEL(LOG(JA_YCV/JA_SHARETV),1)
+ C3704 * DEL(LOG(JA_YCV.-1/JA_SHARETV.-1),1)
+ C3705 * DEL(LOG(JA_YCV.-2/JA_SHARETV.-2),1)
+ C3706 * DEL(LOG(JA_YCV.-3/JA_SHARETV.-3),1)
+ C3707 * JA_D932
+ C3708 * JA_D982C983
+ C3709 * DEL(JA_D993C001,1)
+ CERR * ER2_PER

## 125 ）市街地地価指数

DEL(LOG(JA_PLAND),1) = C3801 * LOG(JA_PLAND.-1/(EXP(P3801) * JA_TIMEV**(P3802) * JA_GDPV**(P3803 * JA_PSHARE**(P3804))
+ C3802 * DEL(LOG(JA_PLAND.-1),1)
+ C3803 * DEL(LOG(JA_M2CD),1)
+ C3804 * DEL(LOG(JA_M2CD.-1),1)
+ C3805 * DEL(LOG(JA_PSHARE),1)
+ C3806 * DEL(LOG(JA_PSHARE.-1),1)
+ C3807 * DEL(LOG(JA_PSHARE.-2),1)
+ CERR * ER2_PLAND

## 126 ）家計株式保有比率

$$ \begin{aligned} \text{DEL}(\text{LOG}(\text{JA\_RSHARE}),1) &= \text{C3901} * 1 \\ &+ \text{C3902} * \text{LOG}(\text{JA\_RSHARE}.-1/\text{JA\_RSHARET}.-1/\text{EXP}(-0.0015082*\text{JA\_TIMEVF})) \\ &+ \text{C3903} * \text{DEL}(\text{LOG}(\text{JA\_RSHARE}.-1),1) \\ &+ \text{C3904} * \text{DEL}(\text{LOG}(\text{JA\_RSHARE}.-2),1) \\ &+ \text{C3905} * \text{DEL}(\text{LOG}(\text{JA\_RSHARE}.-3),1) \\ &+ \text{C3906} * \text{DEL}(\text{LOG}(\text{JA\_RSHARE}.-4),1) \\ &+ \text{C3907} * \text{GR}(\text{JA\_PSHARE},1) \\ &+ \text{C3908} * \text{GR}(\text{JA\_PSHARE}.-1,1) \\ &+ \text{C3909} * \text{JA\_RCD} \\ &+ \text{CERR} * \text{ER2\_RSHARE} \end{aligned} $$

## 127 ) 減価償却の現在価値

JA\_PVDP = (2.302585093/18)*(1-0.1*EXP(-JA\_RGB/100*18))/(JA\_RGB/100+2.302585093/18)

## 128 ）借入資本の使用者費用

JA_UCCDB2 = JA_PIFP@*(1-JA_TT)*(JA_RCD+JA_SLRATIO*JA_RGB)/(1+JA_SLRATIO)+JA_RRFP*400 - P3951*SUM(GRY(JA_PIFP@)*100,0,1)/2)*(1 - JA_TT *JA_PVDP - JA_TINCR)/(1-JA_TT)

## 129 ）自己資本の使用者費用

## 130 ) 資本の使用者費用

JA_UCCPF2 = (1-JA_REQU)*JA_UCCDB2+JA_REQU*JA_UCCDE2

131）海外からの要素所得
$$ \text{DEL}(\text{LOG}(\text{JA\_RTRIV}),1) = \text{C4001} \times 1 + \text{C4002} \times \text{LOG}(\text{JA\_FASSTV}.-2*\text{SUM}(\text{US\_RGB}.-1,0,1)/(2*\text{JA\_RTRIV}.-1)) + \text{C4003} \times \text{DEL}(\text{US\_RGB}.-1,1) + \text{C4004} \times \text{DEL}(\text{LOG}(\text{JA\_FXS}),1) + \text{C4005} \times \text{JA\_D961} + \text{CERR} \times \text{ER2\_RTRIV} $$
JA_BCV = JA_BFV/4 + (JA_RTRIV-JA_PTRIV)/4 + JA_ERRBCV

## 132 ) 海外への要素所得

$$ \begin{aligned}
& \text{DEL}(\text{LOG}(\text{JA\_PTRIV}),1) &= C4101 * 1 \\
& \quad + C4102 * \log(\text{JA\_FLIABV}.-2* \text{SUM}(\text{JA\_RGB}.-1,0,1)/(2* \text{JA\_PTRIV}.-1)) \\
& \quad + C4103 * \text{DEL}(\text{LOG}(\text{JA\_FLIABV}.-1),1) \\
& \quad + C4104 * \text{DEL}(\text{JA\_RGB}.-1,1) \\
& \quad + C4105 * \text{DEL}(\text{JA\_RGB}.-2,1) \\
& \quad + C4106 * \text{DEL}(\text{JA\_RCD}.-2,1) \\
& \quad + C4107 * \text{DEL}(\text{JA\_RCD}.-3,1) \\
& \quad + C4108 * \text{DEL}(\text{LOG}(\text{JA\_FXS}),1) \\
& \quad + C4109 * \text{JA\_D961} \\
& \quad + \text{CERR} * \text{ER2\_PTRIV}
\end{aligned} $$

## 133 ) 对外資產

DEL(LOG(JA_FASSTV),1) = C4201 * 1
+ C4202 * LOG((EXP(P4201+P4202*JA_TIMEV.-1)*JA_GDPV.-1**P4203 *JA_SHARETV.-1**P4204) /JA_FASSTV.-1)
+ C4203 * DEL(LOG(JA_FASSTV.-1),1)
+ C4204 * DEL(LOG(JA_GDPV),1)
+ C4205 * (JA_RGB.-2 - US_RGB.-2)
+ CERR * ER2_FASSTV

## 134 ) 為替レート

$$ \begin{array}{r l} \text{DEL}(\text{LOG}(\text{JA\_FXS}),1) &= C4301 * \log(\text{JA\_FXS}.-1/(\text{JA\_DPI}@.-1/\text{US\_PPI}.-1)) \\ & + C4302 * \text{DEL}(\text{LOG}(\text{JA\_FXS}.-1),1) \\ & + C4303 * \text{DEL}(\text{LOG}(\text{JA\_FXS}.-2),1) \\ & + C4304 * \text{DEL}(\text{LOG}(\text{JA\_FXS}.-3),1) \\ & + C4305 * \text{DEL}(\text{LOG}(\text{JA\_DPI}@/\text{US\_PPI}),1) \\ & + C4306 * (\text{US\_RGB} - \text{JA\_RGB}) \\ & + C4307 * (\text{US\_RGB}.-1 - \text{JA\_RGB}.-1) \\ & + C4308 * (\text{US\_RGB}.-2 - \text{JA\_RGB}.-2) \\ & + C4309 * (\text{US\_RGB}.-3 - \text{JA\_RGB}.-3) \\ & + C4310 * (\text{US\_RGB}.-4 - \text{JA\_RGB}.-4) \\ & + C4311 * \text{DEL}(\text{JA\_SBCV}@\text{GDPV}.-1,4) \\ & + \text{CERR} * \text{ER2\_FXS} \end{array} $$

## 135 ) 经常收支

## 136 ) 累積経常収支

JA_SBCV = JA_SBCV.-1 * JA_RSBCV + JA_BCV

## 137 ) 对外資產評価調整額

$$ \begin{aligned}LOG(JA\_{R}SBCV)&=R44\quad*LOG(JA\_{R}SBCV.-1)\\&+C4401*(1-R44)\\&+C4402*(LOG(JA\_{F}XS/JA\_{F}XS.-1)\\&-R44*LOG(JA\_{F}XS.-1/JA\_{F}XS.-2))\\&+CERR*ER2\_{R}SBCV\\ \end{aligned} $$

138) 对外负债

JA_FLIABV = JA_FASSTV - JA_SBCV

139）经常收支对名目 GDP 比

JA_BCV@GDPV = JA_BCV/JA_GDPV*400

140) 累積經常收支対名目 GDP 比

JA_SBCV@GDPV = JA_SBCV/JA_GDPV*400
## 141 ）総生産稼働率

$$ \begin{array}{r l}

\mathrm{DEL}(\mathrm{JA\_GDPGAP},1) &= C4501 * (\mathrm{JA\_GDPGAP}.-1 - \mathrm{JE\_GDPGAPEQ}.-1) \\

& + C4502 * \mathrm{DEL}((\mathrm{JA\_CP}+\mathrm{JA\_IFP}+\mathrm{JA\_IHP}+\mathrm{JA\_CG}+\mathrm{JA\_IG}+\mathrm{JA\_BF})/\mathrm{JA\_GDPPOT}*100,1) \\

& + C4503 * \mathrm{DEL}(\mathrm{JA\_INP}.-1/\mathrm{JA\_GDPPOT}.-1*100,1) \\

& + C4504 * \mathrm{DEL}(\mathrm{JA\_GDPGAP}.-1,1) \\

& + C4505 * \mathrm{DEL}(\mathrm{JA\_GDPGAP}.-2,1) \\

& + C4506 * \mathrm{DEL}(\mathrm{JA\_GDPGAP}.-3,1) \\

& + C4507 * \mathrm{DEL}(\mathrm{JA\_RRCD}.-1,1) \\

& + C4508 * \mathrm{DEL}(\mathrm{LOG}(\mathrm{JA\_WIPH}.-1/\mathrm{JA\_PCP}.-1),1) \\

& + \mathrm{CERR} * \mathrm{ER2\_GDPGAP}

\end{array} $$

## 142 ）完全雇用 GDP

$$ \begin{array}{r l}{\mathrm{L O G(J A\_{G} D P P O T)}}&{=(1-\mathrm{J A\_{Y} W V B F})\mathrm{^{*}L O G(J A\_{K} F P.-1^{*}C4605)}+}\\ &{\quad\mathrm{J A\_{Y} W V B F}\mathrm{^{*}L O G(J A\_{L} F^{*}(1-J A\_{U} R E Q/100)^{*}J A\_{L} H E Q)}}\\ &{+\mathrm{C4601}*1}\\ &{+\mathrm{C4602}*\mathrm{J A\_{T} I M E V}}\\ &{+\mathrm{C4603}*\mathrm{J A\_{T} M853C}}\\ &{+\mathrm{C4604}*\mathrm{J A\_{T} M934C}}\end{array} $$
ESRI Discussion Paper Series No.258

# Dealing with ZLB in DSGE models An application to the Japanese economy

by

Stéphane Adjemian

and

Michel Juillard

December 2010

Economic and Social Research Institute

Cabinet Office

Tokyo, Japan
# Dealing with ZLB in DSGE models An application to the Japanese economy

Stéphane Adjemian $ ^{*} $ Michel Juillard $ ^{\dagger} $

## Abstract

In this paper we propose an estimation strategy for DSGE models with occasionally binding constraints, such as models with a zero lower bound for the nominal interest rate (ZLB).

The usual likelihood approach is based on a first order approximation of the model around its deterministic steady state. This is not possible when we deal with a model with occasionally binding constraints, because the model is non differentiable everywhere and because, putting this first problem aside, the agents in the approximated model do not anticipate that the economy may hit the zero lower bound in the future.

A medium scaled DSGE model with ZLB is estimated by the Simulated Method of Moments, using the Extended Path approach to simulate artificial time series for the observed variables. The Extended Path approach to simulation of stochastic forward–looking models, takes into account the full nonlinearities of the deterministic part of the model, but ignores the Jensen inequality. The extended path method is well suited for models including the zero lower bound because (contrary to the perturbation method) it does not rely on a strong smoothness assumption and so can handle problems with non differentiabilities. This approach proves to be feasible in practice.

## I ntroduction

Currently, estimation of DSGE models is generally done on the basis of a first order local approximation of the model. However, this approach is very unsatisfactory when the economy is confronted with an occasionally binding
constraint such as the zero lower bound (ZLB) for nominal interest rates, because, with this solution strategy, the agents do not anticipate that the economy may hit the zero lower bound in the future.

A global approximation method would be the best alternative, but its computational burden would be very high for a medium-scaled model and such strategy is not applicable to this day.

In this paper, we try to estimate the model with the Simulated Method of Moments (SMM), using the Extended Path approach (EP) to simulate artificial time series for the observed variables. The Extended Path approach to simulation of stochastic forward–looking models, takes into account the full nonlinearities of the deterministic part of the model, but solves only approximately the effect of future uncertainty by using the expected value of future shocks, zero by construction, instead of computing the expected nonlinear effects of future shocks, therefore ignoring Jensen inequality.

The extended path method is well suited for models including the zero lower bound because (contrary to the perturbation method) it does not rely on a strong smoothness assumption and so can handle problems with non differentiabilities. This approach proves to be feasible in practice.

In the case of the Japanese economy, the ZLB has been binding for almost ten years. It is a major challenge for the utilization of DSGE models in the case of Japan. The objective of this paper is to estimate a medium-scaled DSGE model for the Japanese economy over the recent period. In this paper, we evaluate the ability of a model, that we developed in a previous study (Adjemian and Juillard, 2009), to reproduce the sample frequency of hitting the ZLB, using GDP, consumption, investment, inflation, wages and nominal interest rate as observed variables.

In the first section we introduce briefly the model. The extended path method is presented in section 2 and the simulated method of moments in section 3. Section 4 presents first estimation results and concludes.
## 1 The model

The present model is strongly influenced by Smets and Wouters (2007). It is a closed economy model. Nominal rigidities à la Calvo on price and wage, with indexation on past inflation and steady state inflation, have a strong influence on the monetary transmission mechanism. So, do real rigidities on investment and endogenous capacity utilisation. The model contains a large number of shocks. We don’t exploit all in the present paper.

### 1.1 Households

The economy is populated with a continuum of households $ h \in [0,1] $ . Each household values consumption of a composite good. We write $ C_{t}(h) $ the demand of this good by household h in period t. A household offers as well labor hours. We write $ L_{t}(h) $ the labor supply of household h in period t. Welfare is defined as:

$$ \begin{aligned}\mathcal{W}_{t}(h)&=u_{t}(h)+\beta\mathbb{E}[\mathcal{W}_{t+1}(h)]\\u_{t}(h)&=\frac{\left[C_{t}(h)-\eta\overline{C}_{t-1}\right]^{1-\sigma_{c}}}{1-\sigma_{c}}\exp\left\{\varepsilon_{L,t}\frac{\sigma_{c}-1}{1+\sigma_{l}}L_{t}(h)^{1+\sigma_{l}}\right\}\end{aligned} $$

where $ \varepsilon_{L,t} $ is a shock to labor supply. $ \log \varepsilon_{L,t} $ is an AR exogenous shock process with mean $ \log \tilde{L} $ (this parameter gives us an extra degree of freedom for adjusting the stationary level of hours). We choose this form for the utility function in order to build a model compatible with balanced growth. We assume that utility obtained by household h in period t depends not only on its own consumption but as well on aggregate consumption in previous period, $ \overline{C}_{t-1} = \int_{0}^{1} C_{t-1}(h) \, \mathrm{d}h $ . This is a mechanism of external habits.

The budget constraint of household h, in period t, in real terms, is the following:

$$ \begin{aligned}C_{t}(h)&+p_{I,t}I_{t}(h)=\Biggl\{\frac{B_{t-1}(h)}{P_{t}}-\frac{B_{t}(h)}{P_{t}\varepsilon_{B,t}R_{t}}+(1-\tau_{W,t})\frac{W_{t}^{m}}{P_{t}}L_{t}(h)\\&+r_{t}^{k}z_{t}(h)K_{t-1}(h)+\frac{\mathcal{D}_{1,t}(h)+\mathcal{D}_{2,t}(h)}{P_{t}}\Biggr\}+T_{t}\end{aligned} $$

where $ P_{t} $ is the aggregate price index; $ R_{t} = 1 + i_{t} $ , corresponds to the rate of interest plus one, $ B_{t}(h) $ the nominal value of bonds detained by household h at the end of period t, $ \varepsilon_{t}^{B} $ is the risk premium requested by households
in order to detain the bond; $ \log\varepsilon_{t}^{B} $ is an AR process with zero mean; $ I_{t}(h) $ is investment of h during period t; $ \log p_{I,t} $ is an exogenous shock on the relative price of investment and follows an AR process with zero mean; $ W_{t}^{m} $ is the hourly wage rate received by household h in period t; $ T_{t} $ represents net transfers received by the household during the period; $ \mathcal{D}_{1,t}(h) $ and $ \mathcal{D}_{2,t}(h) $ are the dividends received from firms and from the unions that differentiate household labor supply.

On the resource side, return on physical capital, $ r_{t} $ , is given by

$$ r_{t}^{k}=z_{t}(h)K_{t-1}(h) $$

where the stock of physical capital at date t is

$$ K_{t}(h)=\left(1-\delta(z_{t}(h))\right)K_{t-1}(h)+\varepsilon_{I,t}\left(1-\mathcal{S}\left(\frac{I_{t}(h)}{I_{t-1}(h)}\right)\right)I_{t}(h) $$

$ z_{t}(h)\in[0,1] $ is the rate of utilization of physical capital with steady value $ z^{\star} $ ; the depreciation rate, $ \delta $ , is a function of the rate of utilization that verifies $ \delta(0)=0 $ , $ \delta(1)=1 $ , $ \delta(z)^{\prime}>0 $ for all $ z\in[0,1] $ and we write $ \delta(z^{\star})=\delta^{\star} $ ; $ \varepsilon_{I,t} $ is a random shock to the efficiency of capital accumulation $ \log\varepsilon_{I,t} $ is an AR process with zero mean; function S describes adjustment costs on investment, we assume $ \mathcal{S}(1+g)=0 $ , where g is the rate of growth of investment on the balanced growth path, furthermore $ \mathcal{S}(1+g)^{\prime}=0 $ and $ S^{\prime\prime}>0 $ .

Each household h chooses its consumption, labor supply, bond holdings, investment, and capital utilization rate so as to maximize its inter-temporal utility (1.1) under the budget constraint (1.2) and the law of evolution of physical capital (1.3), taking as given evolution of prices and exogenous variables.

The first order optimality conditions are given by:

$$ \left(C_{t}(h)-\eta\overline{C}_{t-1}\right)^{-\sigma_{c}}\exp\left\{\varepsilon_{L,t}\frac{\sigma_{c}-1}{1+\sigma_{l}}L_{t}(h)^{1+\sigma_{l}}\right\}=\lambda_{t}(h) $$

where $ \lambda_{t}(h) $ is the Lagrange multiplier associated to the real budget constraint,

$$ \lambda_{t}(h)=\beta\varepsilon_{B,t}R_{t}\mathbb{E}_{t}\left[\frac{\lambda_{t+1}(h)}{\pi_{t+1}}\right] $$

where $ \pi_{t+1} \equiv P_{t+1}/P_{t} $ is the inflation rate between period t and $ t+1 $ ,

$$ u_{t}(h)\left(\sigma_{c}-1\right)\varepsilon_{L,t}L_{t}(h)^{\sigma_{l}}=-\lambda_{t}(h)\frac{W_{t}^{m}}{P_{t}}. $$